Finding index-positions after -spatial- matrix multiplication. bsxfun implemented

Question

I need help finding some index-positions of a matrix and two vectors after a complicated matrix multiplication, please bear with me and read what I have first, my question comes at the end.

I have two matrices L1 and L2:

L1 = firstMatrix;
L2 = secondMatrix;

I need to compute the difference (column-wise) of every single value from L1 with all the values of L2, again, in column-wise form, this is done as follows:

step one

lib1 = bsxfun(@minus, L1(:,1)',L2(:,1));
lib1=lib1(:);
lib2 = bsxfun(@minus, L1(:,2)',L2(:,2));
lib2=lib2(:);
lib3 = bsxfun(@minus, L1(:,3)',L2(:,3));
lib3=lib3(:);

At the end I have my new matrix LBR:

LBR = [lib1 lib2 lib3];

Now, I have two vectors alpha and beta -given on a closed domain with same step-size, in this case they are the same-.

alpha = 0:0.1:2;
beta = 0:0.1:2;

I need now to compute the tensor-product, I can do it in two ways:

step two

first way:

alphat1 = kron(alpha,lib1);
alphat2 = kron(alpha,lib2);
alphat3 = kron(alpha,lib3);
T1 = [alphat1 alphat2 alphat3];
betat1 = kron(beta,lib1);
betat2 = kron(beta,lib2);
betat3 = kron(beta,lib3);
T2 = [betat1 betat2 betat3];

Or, the second way, which is by means of the bsxfun from matlab:

val = bsxfun(@times,LBR,permute(alpha,[3 1 2]));
T = reshape(permute(val,[1 3 2]),size(val,1)*size(val,3),[]);

val2 = bsxfun(@times,LBR,permute(beta,[3 1 2]));
T2 = reshape(permute(val2,[1 3 2]),size(val2,1)*size(val2,3),[]);

My problem:

I need to find the min-distance in the following way, first, I have of course three constants:

gama1 = value1;
gama2 = value2;
gama3 = value3;

And the min-distance is computed as follows:

step three

[d,p] = min(((T(:,1)-T2(:,1))-gama1).^2 + ((T(:,2)-T2(:,2))-gama2).^2 +
((T(:,3)-T2(:,3))-gama3).^2);
d = sqrt(d);

I need, very much, the index positions of L1, L2, alpha and beta which are fulfilling this min-distance problem.

I have tried the following:

step four

[minindex_alongL2, minindex_alongL1, minindex_alongalpha, minindex_alongbeta] = 
ind2sub([size(L2,1) size(L1,1) numel(alpha) numel(beta)],p);

But it doesn't work. I would appreciate very much all the help you can provide me!

Thanks in advance.

Answer 1

alpha and beta gets T and T2 respectively. Then you are performing columnwise subtraction between T and T2 and not a subtraction for each element of a column in T against all elements of the same column number in T2. If you would like to perform the latter, you are most probably needed to change the codes from ground up and getting rid of concatenations and extending into multi-dimensional arrays.

Continuing with what you have in your codes, you can at most get joint alpha-beta indices and not separate indices for alpha and beta.

Thus, you can have something like -

[minindex_alongL2, minindex_alongL1, minindex_alongalphabeta] = ind2sub([size(L2,1) size(L1,1) numel(alpha)],p)

Edit 1: Assuming you are inputting values for L1, L2, value1, value2, value3 and row vectors alpha and beta, see if this code works for you -

lib1 = bsxfun(@minus, L1(:,1)',L2(:,1)); %%//'
lib2 = bsxfun(@minus, L1(:,2)',L2(:,2)); %%//'
lib3 = bsxfun(@minus, L1(:,3)',L2(:,3)); %%//'

t1 = cat(3,lib1,lib2,lib3);
t2 = permute(alpha,[4 3 1 2]);
T = bsxfun(@times,t1,t2);

t22 = permute(beta,[4 3 1 2]);
T2 = bsxfun(@times,t1,t22);

gama1 = value1;
gama2 = value2;
gama3 = value3;

mat1 = bsxfun(@minus,T,permute(T2,[1 2 3 5 4]));
mat2 = bsxfun(@minus,mat1,permute([gama1;gama2;gama3],[3 2 1]));
mat2 = squeeze(sum(mat2,3));

[d,p] = min(mat2(:));
d = sqrt(d);

[minindex_alongL2, minindex_alongL1, minindex_alongalpha, minindex_alongbeta] = ind2sub([size(L2,1) size(L1,1) numel(alpha) numel(beta)],p)